Sala Riunioni (Dip. Matematica)

Seminario di geometria - Higher analytic stacks and GAGA theorems

Relatore: 
Mauro Porta

Abstract. I will survey a recent joint work with T.Y. Yu (preprint availabe at arXiv 1412.5166). In this article, we lay the foundations of higher analytic geometric stacks, where "analytic" means both complex-analytic and rigid-analytic. We subsequently introduce the fundamental notion of proper morphisms between such objects and prove a generalization of Grauert - Remmert finiteness theorem for proper higher direct images. As an application, we deduce GAGA theorems for higher stacks.

Data Seminario: 
Wednesday, January 21, 2015
Aula: 
Sala Riunioni (Dip. Matematica)
Ora Fine: 
Saturday, January 1, 0000 - 15:30
Affiliazione: 
Universitè Paris Jussieu
Ora Inizio: 
Saturday, January 1, 0000 - 14:30

Symmetries of hyperbolic 4-manifolds

Tipo Seminario: 

We will introduce a construction which produces a family of arithmetic, non-compact hyperbolic 4-manifolds, such that every finite group G is realized as the symmetry group of some member of this family. This allows us to obtain asymptotic bounds which relate the order of a finite group G with the minimal volume of a hyperbolic 4-manifold realizing G as its symmetry group.
The construction uses very accessible techniques: basic hyperbolic geometry on one hand, and the combinatorial properties of simplicial complexes on the other.
 

Data Seminario: 
Wednesday, January 14, 2015
Relatore: 
Leone Slavich
Ora Fine: 
Saturday, January 1, 0000 - 16:00
Aula: 
Sala Riunioni (Dip. Matematica)
Ora Inizio: 
Saturday, January 1, 0000 - 15:00

Real closed rings and o-minimality

Tipo Seminario: 
Relatore: 
Marcus Tressl

Real closed rings are rings that occur frequently in the study of o-minimal fields (such as the real field).
Examples are rings of continuous functions that have algebraic graph, or valuation rings of o-minimal fields.
The talk will give an introduction to the subject from scratch and describe recent work
on algebraic and decidability questions for various real closed rings.

Data Seminario: 
Tuesday, December 16, 2014
Aula: 
Sala Riunioni (Dip. Matematica)
Ora Fine: 
Saturday, January 1, 0000 - 15:00
Affiliazione: 
University of Manchester
Ora Inizio: 
Saturday, January 1, 0000 - 13:30

Infinitesimal Hilbert problem

Relatore: 
Sergei Yakovenko
The infinitesimal Hilbert problem addresses limit cycles of planar polynomial vector field, which appear by a small non-conservative perturbation of an integrable (Hamiltonian) system. Their number is closely related to the number of algebraic level ovals of a bivariate polynomial corresponding to zero periods of a polynomial 1-form.
Data Seminario: 
Monday, December 15, 2014
Aula: 
Sala Riunioni (Dip. Matematica)
Ora Fine: 
Saturday, January 1, 0000 - 16:30
Affiliazione: 
Weizmann Institute and Universita di Pisa
Ora Inizio: 
Saturday, January 1, 0000 - 15:30

Seminario di geometria - Invarianti coomologici per stack di curve lisce

Relatore: 
Roberto Pirisi

abstract:
Gli invarianti coomologici sono un analogo aritmetico alle classi caratteristiche in topologia, in cui la coomologia singolare è rimpiazzata dalla coomologia di Galois, e gli spazi topologici da spettri di campi.
Dato un gruppo algebrico affine G, un invariante coomologico per G è un modo di assegnare funtorialmente a ogni G-fibrato principale sullo spettro di un campo k un elemento della coomologia di Galois di k. Questi invarianti formano un anello graduato, che è stato calcolato per molti gruppi da diversi autori, tra cui Serre, Merkujev e Rost.

Data Seminario: 
Wednesday, December 3, 2014
Aula: 
Sala Riunioni (Dip. Matematica)
Ora Fine: 
Saturday, January 1, 0000 - 15:00
Affiliazione: 
Scuola Normale Superiore
Ora Inizio: 
Saturday, January 1, 0000 - 14:00

Seminario di Geometria - Curves with A_k - singularities on K3 surfaces

Relatore: 
Andreas Leopold Knutsen - University of Bergen
Let (S,H) be a general primitively polarized K3 surface. I will talk about a joint work with Concettina Galati, where we prove the existence of curves in the complete linear system |nH| with $A_k$-singularities and living in families of the "expected dimension". This generalizes results in the nodal case of Mumford for n=1 and Chen for n>1. The proof is by degenerating the K3 surface to a union of rational normal scrolls and deform a higher order tacnode on a curve on the degerated surface.
Data Seminario: 
Wednesday, November 26, 2014
Aula: 
Sala Riunioni (Dip. Matematica)
Ora Inizio: 
Saturday, January 1, 0000 - 13:30
Ora Fine: 
Saturday, January 1, 0000 - 14:30

Seminario di O-MINIMALITA' - Counting points and o-minimality

Relatore: 
Margaret Thomas - Universitat Konstanz, Germany

The results surveyed in this talk are part of a wider, flourishing interaction between diophantine geometry and o-minimality. The central problem is to bound the density of rational and algebraic points on certain subsets of the reals. Beginning with work by Bombieri and Pila in the 1980s, a key breakthrough came from the application of o-minimality to the problem by Pila and Wilkie in 2006. This, in particular thanks to a strategy utilizing their result developed by Pila and Zannier, has found many significant applications to important open problems in number theory.

Data Seminario: 
Friday, November 14, 2014
Aula: 
Sala Riunioni (Dip. Matematica)
Ora Inizio: 
Saturday, January 1, 0000 - 10:00
Ora Fine: 
Saturday, January 1, 0000 - 11:00

Counting points and o-minimality

Tipo Seminario: 
Relatore: 
Margaret Thomas

The results surveyed in this talk are part of a wider, flourishing interaction between diophantine geometry and o-minimality. The central problem is to bound the density of rational and algebraic points on certain subsets of the reals. Beginning with work by Bombieri and Pila in the 1980s, a key breakthrough came from the application of o-minimality to the problem by Pila and Wilkie in 2006. This, in particular thanks to a strategy utilizing their result developed by Pila and Zannier, has found many significant applications to important open problems in number theory.

Data Seminario: 
Friday, November 14, 2014
Aula: 
Sala Riunioni (Dip. Matematica)
Ora Fine: 
Saturday, January 1, 0000 - 11:30
Affiliazione: 
University of Konstanz
Ora Inizio: 
Saturday, January 1, 0000 - 10:00

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